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On the Expected Discounted Penalty Function Using Physics-Informed Neural Network 利用物理信息神经网络研究预期贴现惩罚函数
IF 1.4 4区 数学
Journal of Mathematics Pub Date : 2023-12-28 DOI: 10.1155/2023/9950023
Jiayu Wang, Houchun Wang
{"title":"On the Expected Discounted Penalty Function Using Physics-Informed Neural Network","authors":"Jiayu Wang, Houchun Wang","doi":"10.1155/2023/9950023","DOIUrl":"https://doi.org/10.1155/2023/9950023","url":null,"abstract":"We study the expected discounted penalty at ruin under a stochastic discount rate for the compound Poisson risk model with a threshold dividend strategy. The discount rate is modeled by a Poisson process and a standard Brownian motion. By applying the differentiation method and total expectation formula, we obtain an integrodifferential equation for the expected discounted penalty function. From this integrodifferential equation, a renewal equation and an asymptotic formula satisfied by the expected discounted penalty function are derived. In order to solve the integrodifferential equation, we use a physics-informed neural network (PINN) for the first time in risk theory and obtain the numerical solutions of the expected discounted penalty function in some special cases of the penalty at ruin.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139052639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Well-Posedness in Variable-Exponent Function Spaces for the Three-Dimensional Micropolar Fluid Equations 三维微波流体方程在变指数函数空间中的好求解性
IF 1.4 4区 数学
Journal of Mathematics Pub Date : 2023-12-26 DOI: 10.1155/2023/4083997
Muhammad Zainul Abidin, Muhammad Marwan, Naeem Ullah, Ahmed Mohamed Zidan
{"title":"Well-Posedness in Variable-Exponent Function Spaces for the Three-Dimensional Micropolar Fluid Equations","authors":"Muhammad Zainul Abidin, Muhammad Marwan, Naeem Ullah, Ahmed Mohamed Zidan","doi":"10.1155/2023/4083997","DOIUrl":"https://doi.org/10.1155/2023/4083997","url":null,"abstract":"In this paper, we work on the Cauchy problem of the three-dimensional micropolar fluid equations. For small initial data, in the variable-exponent Fourier–Besov spaces, we achieve the global well-posedness result. The Littlewood–Paley decomposition method and the Fourier-localization technique are main tools to obtain the results. Moreover, the results discussed in our work show the Gevrey class regularity of solution to the Cauchy problem of micropolar fluid equations.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"22 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139052682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization 高维 HJB 方程渐近分析在投资组合优化中的应用
IF 1.4 4区 数学
Journal of Mathematics Pub Date : 2023-12-21 DOI: 10.1155/2023/3399493
Lei Hu
{"title":"Application of Asymptotic Analysis of a High-Dimensional HJB Equation to Portfolio Optimization","authors":"Lei Hu","doi":"10.1155/2023/3399493","DOIUrl":"https://doi.org/10.1155/2023/3399493","url":null,"abstract":"In this paper, we consider a portfolio optimization problem where the wealth consists of investing into a risky asset with a slow mean-reverting volatility and receiving an uncontrollable stochastic cash flow under the exponential utility. The Hamilton–Jacobi–Bellman equation formulated from the optimal investment problem is a high-dimensional nonlinear partial differential equation and difficult to find its analytical or numerical solutions. The paper provides a tractable asymptotic approach which treats the initial problem as a perturbation around the constant volatility problem. In this paper, we present a formal derivation of asymptotic approximation and prove the accuracy of the value function. Moreover, an illustrative example is provided to assess our approximate strategy and value function.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"20 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138824741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Retracted: Research on the Spread Path and Evolution Causes of Oral Language in the Digital Era 撤回：数字时代口语的传播路径和演变原因研究
IF 1.4 4区 数学
Journal of Mathematics Pub Date : 2023-12-20 DOI: 10.1155/2023/9878209
Journal of Mathematics
{"title":"Retracted: Research on the Spread Path and Evolution Causes of Oral Language in the Digital Era","authors":"Journal of Mathematics","doi":"10.1155/2023/9878209","DOIUrl":"https://doi.org/10.1155/2023/9878209","url":null,"abstract":"<jats:p />","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"123 35","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138953713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Retracted: Classification and Analysis of College Students’ Skills Using Hybrid AI Models 撤回：利用混合人工智能模型对大学生的技能进行分类和分析
IF 1.4 4区 数学
Journal of Mathematics Pub Date : 2023-12-20 DOI: 10.1155/2023/9842979
Journal of Mathematics
{"title":"Retracted: Classification and Analysis of College Students’ Skills Using Hybrid AI Models","authors":"Journal of Mathematics","doi":"10.1155/2023/9842979","DOIUrl":"https://doi.org/10.1155/2023/9842979","url":null,"abstract":"<jats:p />","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"62 21","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138957063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Retracted: Optimization Algorithm of Logistics Transportation Cost of Prefabricated Building Components for Project Management 撤回：面向项目管理的预制建筑构件物流运输成本优化算法
IF 1.4 4区 数学
Journal of Mathematics Pub Date : 2023-12-20 DOI: 10.1155/2023/9858351
Journal of Mathematics
{"title":"Retracted: Optimization Algorithm of Logistics Transportation Cost of Prefabricated Building Components for Project Management","authors":"Journal of Mathematics","doi":"10.1155/2023/9858351","DOIUrl":"https://doi.org/10.1155/2023/9858351","url":null,"abstract":"<jats:p />","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"24 11","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138955168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Retracted: Design of Enterprise Economic Information Management System Based on Big Data Integration Algorithm 撤回：基于大数据整合算法的企业经济信息管理系统设计
IF 1.4 4区 数学
Journal of Mathematics Pub Date : 2023-12-20 DOI: 10.1155/2023/9876921
Journal of Mathematics
{"title":"Retracted: Design of Enterprise Economic Information Management System Based on Big Data Integration Algorithm","authors":"Journal of Mathematics","doi":"10.1155/2023/9876921","DOIUrl":"https://doi.org/10.1155/2023/9876921","url":null,"abstract":"<jats:p />","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"18 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138994351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Retracted: Text Knowledge Acquisition Method of Collaborative Product Design Based on Genetic Algorithm 撤回：基于遗传算法的产品协同设计文本知识获取方法
IF 1.4 4区 数学
Journal of Mathematics Pub Date : 2023-12-20 DOI: 10.1155/2023/9894560
Journal of Mathematics
{"title":"Retracted: Text Knowledge Acquisition Method of Collaborative Product Design Based on Genetic Algorithm","authors":"Journal of Mathematics","doi":"10.1155/2023/9894560","DOIUrl":"https://doi.org/10.1155/2023/9894560","url":null,"abstract":"<jats:p />","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"32 16","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138955894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Retracted: Evaluation Algorithm of Labor Legal Effectiveness for Affirmative Action against Gender Discrimination 撤回：反性别歧视平权行动的劳动法律效力评估算法
IF 1.4 4区 数学
Journal of Mathematics Pub Date : 2023-12-20 DOI: 10.1155/2023/9892024
Journal of Mathematics
{"title":"Retracted: Evaluation Algorithm of Labor Legal Effectiveness for Affirmative Action against Gender Discrimination","authors":"Journal of Mathematics","doi":"10.1155/2023/9892024","DOIUrl":"https://doi.org/10.1155/2023/9892024","url":null,"abstract":"<jats:p />","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"56 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138957109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Retracted: Data Mining and Analysis of the Compatibility Law of Traditional Chinese Medicines Based on FP-Growth Algorithm 撤回：基于FP-Growth算法的中药相克规律数据挖掘与分析
IF 1.4 4区 数学
Journal of Mathematics Pub Date : 2023-12-20 DOI: 10.1155/2023/9761056
Journal of Mathematics
{"title":"Retracted: Data Mining and Analysis of the Compatibility Law of Traditional Chinese Medicines Based on FP-Growth Algorithm","authors":"Journal of Mathematics","doi":"10.1155/2023/9761056","DOIUrl":"https://doi.org/10.1155/2023/9761056","url":null,"abstract":"<jats:p />","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"41 24","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138957208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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